# Experimental techniques

The laser-like properties of the X-ray beams generated by the European XFEL will enable completely new experiments in materials science. In particular for techniques relying on the high coherence of the X-ray beam, the MID station will offer extended capabilities compared to present state-of-the-art facilities. In combination with the exceptional flux and the ultra-short pulses of the X-ray laser, it will be possible to investigate materials with unprecedented resolution in space and time. The design of the MID station allows to perform different experimental techniques with the highest performance capabilites.

#### Coherent Diffraction Imaging (CDI)

The MID instrument will provide a platform for coherent X-ray diffractive imaging experiments. The experiments require oversampling of the speckle patterns for inverting the images together with a large field-of-view to reach as high Q as possible. This requires a modular scattering geometry and the possibility of varying the sample-detector distance. At the MID station the goal is to visualize not only shape information of nano- and micro-sized objects but also extracting quantitative information such as electron density, strain field, and chemical compositions. The use of different excitation sources available (e.g. optical laser, pulsed magnetic setups, X-ray Split & Delay Line) enables time-resolved pump-probe CDI experiments on the femtosecond time scale. Ptychography will also be attempted on samples far from the damage threshold.

#### X-ray Photon Correlation Spectroscopy (XPCS)

The study of structural dynamics by X-ray photon correlation spectroscopy (XPCS) provides a tool for characterizing and understanding equilibrium and non-equilibrium processes of materials. Due to the interference of coherent X-ray laser light scattered by the sample, a speckle pattern is generated in the far-field. The speckle pattern evolves as the structure of the sample changes and hence dynamic processes can be mapped out according to the relaxation time of the intensity autocorrelation function at different wave vectors. The unprecedented coherent flux of the European XFEL allows access to faster relaxations and smaller length scales than previously possible. For instance, it will become possible to study surface and interface dynamics at the atomic and molecular scale by X-ray scattering. In addition, the option to perform XPCS at photon energies up to 25 keV allows probing dynamics at buried liquid–liquid and liquid–solid interfaces. Self-organization, self-assembly, and growth of nano-particles could be followed by coherent X-ray scattering allowing kinetics and dynamics studies of such processes at interfaces with unprecedented time resolution.

#### X-ray Cross Correlation Analysis (XCCA)

A main difference between liquids and glasses compared to crystalline materials is the lack of long range order. Nevertheless, local order and hidden symmetries can exist in such disordered systems and coherent X-ray scattering enables the possibility of analyzing speckle patterns for such symmetries via XCCA. The angular correlation of intensities at momentum transfers Q and Q’ can be calculated according to

${C}_{q}\left(\Delta \right)=\genfrac{}{}{0.1ex}{}{〈I\left(Q,\varphi \right)I\left(Q,\varphi +\Delta \right){〉}_{\varphi }-〈I\left(Q,\varphi \right){〉}_{\varphi }^{2}}{〈I\left(Q,\varphi \right){〉}_{\varphi }^{2}}$

A Fourier analysis of the resulting Δ-dependent angular correlation function CQ(Δ) can reveal the dominant symmetries and local ordering. Further developments of XCCA aim to the full spatial reconstruction of nanoobjects, of which several identical entities are present in the scattering volume. Therefore, XCCA might additionally be used to increase the signal-to-noise ratio in 3D reconstruction and imaging applications.

#### X-ray Speckle Visibility Spectroscopy (XSVS)

Information about the dynamical evolution of systems can also be revealed by a visibility analysis of the speckle patterns obtained by a statistical analysis of the photon distribution. The probability of measuring one single photon in a pixel P(k=1), many photons P(k=N), or no photon P(k=0), follows the Poisson-Gamma-Distribution according to:

${P}_{M}\left(k\right)=\genfrac{}{}{0.1ex}{}{\Gamma \left(k+M\right)}{\Gamma M\right)\Gamma \left(k+1\right)}{\left(1+\genfrac{}{}{0.1ex}{}{M}{〈k〉}\right)}^{-k}{\left(1+\genfrac{}{}{0.1ex}{}{〈k〉}{M}\right)}^{-M}$

Hence, statistical analysis of a single image provides direct access to the contrast of the speckle pattern β = 1/M through the measurable quantities: average intensity per pixel and P(k). The application of this method to study dynamics is mainly realized by two different techniques: Variation of the acquisition time T of the speckle images or summing of pairs of images taken with a time difference Δt. In both cases the contrast of the speckles decreases with increasing T or Δt if the scatterers move during the respective times.

In order to access ns-fs dynamics, a sequential acquisition mode like in XPCS is most likely not possible due to detector limitations. Here, XSVS can be used to reach such fast time scales in combination with split and delay line setups.

#### Pump-probe/Time-resolved X-ray Scattering

The exceptional temporal properties of the XFEL pulses with the distinguished time structure and very high peak flux will enable new experimental possibilities for time resolved and pump-probe X-ray scattering experiments. Many different experimental realisations are already today succesfully employed at third-generation synchrotrons sources, however with the constant need of higher flux. Therefore, the MID instrument is designed to enable many different experimental realisations with various detector configurations and a multi-purpose SAXS/WAXS chamber to host different setups, such as optical pump-probe, magnetic field quenching, stopped-flow devices or rapid evaporational cooling.